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Examples oforthonormal
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Such anorthonormalset can be built out of the vacuum using the creation operators.
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The final result is anorthonormalset of basis vectors.
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To show this, we recall a basic result on compact operators andorthonormalsystems.
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In our theory, "true" and "false" are represented byorthonormalvectors, which thus span a subset of twodimensional space represented by a unit square.
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It will then take the values +1 on allorthonormalbases.
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The estimate (1.9.1) rests on some fundamental estimates for the best basis approximation of finite-dimensional hypercubes usingorthonormalbases.
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Since this is true for anyorthonormalbasis, we may average over all of them.
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This description makes use of twoorthonormalbasis sets.
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In particular, we determine an algebraic n-form, unique up to sign, by requiring it to take the value 1 on someorthonormalbasis.
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We may define an inner product in such a way that the ai form anorthonormalbasis.
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It is made with a finite number of one-dimensional edges parallel to the directions of the vectors of the canonicalorthonormalbasis and a finite number of vertices.
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The free parameters of the arbitrary possible choices for theorthonormal(symplectic) basis are ' 'hidden' ' in these ' 'initial' ' vectors.
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In addition, if the basis vectors form anorthonormalset, the overlap matrix will be the identity matrix.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Consider the case of rectangular coordinate systems withorthonormalbases only.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.The following results are true fororthonormalbases, not orthogonal ones.
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Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.Physicists commonly regard a density operator as being represented by a (possibly infinite) density matrix relative to someorthonormalbasis.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.Orthonormalbases are convenient to work with because the inner product of two vectors have simple expressions.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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